Prime Factorization Calculator takes a number as input, and finds all the prime factors of the given number.
Inputs
Sample inputs
n: 10
n: 620
n: 20500
Steps for Prime Factorization
The following is a step-by-step approach to find the prime factorization of a given composite number.
Start with the smallest prime number, which is 2.
Divide the given number by 2. If it divides evenly (with no remainder), then 2 is a prime factor. Repeat this step until the composite number is no longer divisible by 2.
Move on to the next prime number (3), and repeat the division process.
Continue this process with subsequent prime numbers until the composite number is reduced to 1 or a prime number.
Examples - How to use Prime Factorization Calculator
1. Find the prime factors of the number 120.
Solution
Given:
n = 120
Computing Prime Factors:
We will check if the given number is divisible by the prime numbers starting from 2 recursively and express the given number as the multiplication of prime factors.
120 is divisible by the prime number 2. (120=2×60)
120 = 2 × 60
60 is divisible by the prime number 2. (60=2×30)
120 = 2 × 2 × 30
30 is divisible by the prime number 2. (30=2×15)
120 = 2 × 2 × 2 × 15
15 is not divisible by the prime numbers: 2; but divisible by the prime number 3. (15=3×5)
120 = 2 × 2 × 2 × 3 × 5
The last 5 itself is a prime number.
Therefore, Prime Factorization of given number is completed.
Result:
The prime factorization of given number 120 is:
120 = 2 × 2 × 2 × 3 × 5
2. Find the prime factors of the number 35.
Solution
Given:
n = 35
Computing Prime Factors:
We will check if the given number is divisible by the prime numbers starting from 2 recursively and express the given number as the multiplication of prime factors.
35 is not divisible by the prime numbers: 2, 3; but divisible by the prime number 5. (35=5×7)
35 = 5 × 7
The last 7 itself is a prime number.
Therefore, Prime Factorization of given number is completed.
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